Here is the full list of all 13 Dream Catcher achievements.
Win the first level
Win the doggy level
Win the bat wings level
Win the Pigeon level
Win the night dragon level
Win the tentacle level
Win the oversize level
Win the angel level
Win the devil level
Win the angel level in hard mode
Win the devil level in hard mode
Victory without detonate any bombs
Continuously detonate 3 bombs